Cant delete background image
You have two separate 3D views, one on the left and one on the right. Each 3D view has it's own properties panel with its own settings (including background images). You have the properties panel open for the 3D view on the right, but you are wanting to edit the properties for the 3D view on the left. 

Press N while your cursor is in the left 3D view to open its properties panel and remove/change the background images from there.